The jack on the mixamp is a headset jack (mic and headphone in one plug). the other jack is for the xbox controller only. The Y splitter splits the headset jack into a mic jack and headphone jack so you can use a PC headset that has a mic and headphone jack with the mixamp. Additionally you can't use a stereo Y splitter with the mixamp and expect it to split the mic and headphone audio.

Sorry for the double post. Thought I hit edit.
Actually Phos, you're wrong. The other connection is the controller input for the 360. Without that cable that goes from the Mixamp to the 360's controller, you don't get voice chat.
There is no need for two inputs, as the A30/A40 have all come with the mic/audio in one line, with a special connector cable that goes to the Mixamp.
You need a Y cable, unless you have an Astro Headset.

Yes, you need a 3.5mm male to RCA male cable between the Mixamp and Receiver (or 3.5mm male/male + a 3.5mm female to RCA male), and plug it into one of your AUX Ins. Assuming your AUX ins are the typical ReD/White RCA inputs.Edited by Mad Lust Envy - 8/2/12 at 8:35pm

It's from China, and I get it here in the US. Not sure where you're from, but for the $3 or so, it's a very low risk, high reward gamble. Regardless of forgetting it or not, it's gonna take a long time for it to reach you, so don't stress about that.

My clip doesn't have the branding on there, unlike the image, but it is the same mic.Edited by Mad Lust Envy - 8/2/12 at 9:47pm

Does the same theory apply to all amps, such as my O2, or only his receiver?

To all amps.

You'll come to the same conclusion by trial and error: if you put your MixAmp at 20%, connect it to an O2, you'll find you have to crank the O2 volume quite high to reach the same decibel level (by estimation, not measurement).

It's a more efficient setup to crank the MixAmp high and use the second amp to attenuate.